Consumers have become addicted to credit cards with generous rewards programs. Retailers are trying to cut them off.

Large merchants including Amazon.com Inc., Target Corp. and Home Depot Inc. are pushing for the right to reject some rewards credit cards, which typically carry higher fees for merchants. They are likely to opt out of a roughly $6.2 billion settlement Visa Inc., Mastercard Inc. and several large banks recently reached with merchants and continue to make their case in court, according to people familiar with...